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Search: id:A138757
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| 2, 2, 2, 7, 11, 3, 13, 17, 5, 19, 23, 7, 29, 29, 7, 31, 37, 11, 37, 41, 11, 43, 47, 13, 53, 53, 13, 59, 59, 17, 61, 67, 17, 67, 71, 19, 73, 79, 19, 79, 83, 23, 89, 89, 23, 97, 97, 29, 97, 101, 29, 103, 107, 29, 109, 113, 29, 127, 127, 31, 127, 127, 31, 127
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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This can be considered as the analogue of the Collatz (or 3n+1) map on the set of primes, see A138751 and A138754 for details.
Numbers 0,1,2 go immediately to the unique fixed point 2, all others end up in the cycle 7 -> 17 -> 11 -> 7, after a number of iterations given by A138753(A138757(n))-1 (= A138753(n)-2 if n is prime).
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LINKS
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Georges Brougnard, Definition of GB-sequences.
Index entries for sequences related to 3x+1 (or Collatz) problem
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FORMULA
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A138757(n)=A007918(A138750(n)) ; for p prime, A138757(p)=A138751(A000720(p))
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EXAMPLE
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a(7) = 17 since 7 = 1 (mod 3), thus A138750(7) = 2*7 = 14, nextprime(14) = 17.
a(11) = 7 since 11 = 2 (mod 3), thus A138750(11) = ceil(11/2) = 6, nextprime(6) = 7.
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PROGRAM
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(PARI) A138757(n)=nextprime(if(n%3==2, (n+1)\2, 2*n))
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CROSSREFS
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Cf. A124123, A138750-A138756, A007918.
Sequence in context: A029610 A094246 A023573 this_sequence A158927 A121258 A087421
Adjacent sequences: A138754 A138755 A138756 this_sequence A138758 A138759 A138760
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KEYWORD
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easy,nonn
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AUTHOR
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M. F. Hasler (www.univ-ag.fr/~mhasler), Apr 04 2008
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